{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression with a Neural Network mindset\n",
    "\n",
    "Welcome to your first (required) programming assignment! You will build a logistic regression classifier to recognize  cats. This assignment will step you through how to do this with a Neural Network mindset, and so will also hone your intuitions about deep learning.\n",
    "\n",
    "**Instructions:**\n",
    "- Do not use loops (for/while) in your code, unless the instructions explicitly ask you to do so.\n",
    "\n",
    "**You will learn to:**\n",
    "- Build the general architecture of a learning algorithm, including:\n",
    "    - Initializing parameters\n",
    "    - Calculating the cost function and its gradient\n",
    "    - Using an optimization algorithm (gradient descent) \n",
    "- Gather all three functions above into a main model function, in the right order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Packages ##\n",
    "\n",
    "First, let's run the cell below to import all the packages that you will need during this assignment. \n",
    "- [numpy](www.numpy.org) is the fundamental package for scientific computing with Python.\n",
    "- [h5py](http://www.h5py.org) is a common package to interact with a dataset that is stored on an H5 file.\n",
    "- [matplotlib](http://matplotlib.org) is a famous library to plot graphs in Python.\n",
    "- [PIL](http://www.pythonware.com/products/pil/) and [scipy](https://www.scipy.org/) are used here to test your model with your own picture at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import h5py\n",
    "import scipy\n",
    "from PIL import Image\n",
    "from scipy import ndimage\n",
    "from lr_utils import load_dataset\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 2 - Overview of the Problem set ##\n",
    "\n",
    "**Problem Statement**: You are given a dataset (\"data.h5\") containing:\n",
    "    - a training set of m_train images labeled as cat (y=1) or non-cat (y=0)\n",
    "    - a test set of m_test images labeled as cat or non-cat\n",
    "    - each image is of shape (num_px, num_px, 3) where 3 is for the 3 channels (RGB). Thus, each image is square (height = num_px) and (width = num_px).\n",
    "\n",
    "You will build a simple image-recognition algorithm that can correctly classify pictures as cat or non-cat.\n",
    "\n",
    "Let's get more familiar with the dataset. Load the data by running the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading the data (cat/non-cat)\n",
    "train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We added \"_orig\" at the end of image datasets (train and test) because we are going to preprocess them. After preprocessing, we will end up with train_set_x and test_set_x (the labels train_set_y and test_set_y don't need any preprocessing).\n",
    "\n",
    "Each line of your train_set_x_orig and test_set_x_orig is an array representing an image. You can visualize an example by running the following code. Feel free also to change the `index` value and re-run to see other images. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = [1], it's a 'cat' picture.\n"
     ]
    },
    {
     "data": {
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OA6z+f+KI3ouffkxTL66kbFry9EUlMCnVbf8lIuYwKdFb1ryZMXPgohDRy97m\nzID0UHQ/zpwiztYMnt791uWeuO4bX0QKIvIlEfmGiDwrIr/U/vweEXlKRE6LyB+ISO56fUVERLwy\nMIioXwPw7hDCmwA8BOB9IvIIgF8B8GshhPsAbAB47PYNMyIi4lZikNx5AcA1mTfb/gsA3g3gJ9qf\nfxzALwL4rQH62/vvudfYI6/HOd21g4s7bIYRU7ZXa5AXW9L0oq3WlXZUnPf8bbNzanq6++77TJ2k\nVMQ8+8LXTd3ahgYBtci0Nz5uyTbqO2qKEp+SqqFj5vG3HKlINq9zV8jb8U/PqLmMVZXg5oPTRKXd\nK2Q8r+I939uKC/QpkKddyo3j5F0aVHPyTW/slC8+a4XLOo1LMlZd4NRYnMeq7LwtOfOvJxVheDG9\n16N5kNwQ5vnuJ/VTQJA4c+FBA3gG2twTkXQ7U+4qgM8BeAnAZlA/0GUAd/Q6PyIi4pWFgRZ+CKEZ\nQngIwEkAbwXwukEvICKPi8jTIvL0kAhEIyIiroMDmfNCCJsAPg/gbQBmROSa/HgSwIUe5zwRQng4\nhPDwbXa6i4iIGBDX1fFF5AiARghhU0TGALwXext7nwfwowA+AeCDAD59c0Nhl91+A+pX1buy14+O\nJ5BMp7Uhc+cDwMysEkDkCqp35wtWB2dSzoVJq7dWr2qUWdj4kql74ayaD9eqOo5i3uq0nGJuatzq\ntGXy4C2TV6rfr2BX3FbLfs8Cp7jmCDynnwcKY5so2EdpklJZl2nfQcYt2UbIqEkzlbHz+IY3nuqU\nN3Y1knFj0/Lqb22rObVSsubTRk11eSYRLRRcmuz0/hGJgEt5PWjmam+yu5G9Ke8eTBtV3nW403hA\nsXoQO/5xAB8XkTT2JIRPhhA+KyLPAfiEiPwXAF8D8NGBrhgREXHoGGRX/5sA3rzP52ewp+9HRES8\nyjB0z71rZoduSYW96QaEWDGdeeW6RKGeJhNPIKFiXcqJxzOzmlLrrlO6v5kfc+YlilTLOxPVax7U\n8+57u/X4+/ZHNTptlSLJdhNrskNNTYlTzhMuO6a3lGdnq2K/C3vhcWQaAAjxDjbJhOm9BDl994RL\ncT1Bc/J9j6qn3T3f+bBp97E/W+6Ui85s+Y/e/mCnfPaimvZSORut2CKyjVrdkookNHesqZQrVl3g\n52CsaO9Zi56DZuLVHS0PyNHRZULudVqXr2W/C7TrPIlIL0Rf/YiIEURc+BERI4hDTKElPY/8Djwf\npynjacq1S1EQTcp5cLVI5GMCiVTadlIlj65Wzop8HDiTkHfXRN7uEOeyGuRSnLKkEUlKz1t47UOm\n7r7X6+766b9b04qUFV/H84sONL/xAAAfZUlEQVSd8nRl1dTVaAc6U1SRuNqw6oKQgJlxhCOB1IAs\nBdFknAUkoRvj+Qlfc5f6c/3UT393p3zqTe8z7U69/jQNyoqy2fy9nfLqus7NuiMEuUr8hLWaFeFT\n5FKYp2cn6wKTAo0/Kbm5Yo8896o0Tn79JPHeVQPv9xvLQJfYL+3zB9vVj2/8iIgRRFz4EREjiLjw\nIyJGEIen43v9nD7wenc2p3pmcVz16UzWmnXYCy+ft3XsqcY8+A3PKU+6nifbrBCxZY0INqvVommX\ny6lZqly3OleGlMQXL0ybuh/+/rd0yk+9+BXt3/Hq/9Q/faRTPt46b+p+7/e/1ilf3tXvlkk7PZ7m\nO3FpuNlExfcl6/R4pvQPKbunMnPknk75i1/W89ZaF0277/ruH+iUz563XnfPPrPUKV++qibMs8vn\nTLvSFhGflCxpSYbMjMYc6UhF6hUyabroPPZeTBoucu+G4k/6pIi7ke5u4Lz4xo+IGEHEhR8RMYI4\nhGy5e0JJytni2JspX7Bi+ti4em0Vx7RcKE7AgrPD2pommeY4IKNcsaYhm/HUinVVkm0bZTUb5Sgt\nFgDMz+q4Vi4tm7oSEVRUStZc+Og71FPt5/+1zsHaphWB//k/Uw/q1dNfNXV3fFG9AbfPkldcyao0\npaoeV514vHZFswRXqzo/4nkSOatuzqo7UpzvlFfKKvaf/by91l1n/r5TzhdnTN1Ly5c75eVlVWl2\ntjdMu0KWTXbWTFcmzsBA+Q5Kjicx4QzEsEgoyOhWhJZLD1PcXv+DXcAHpN0WIo6IiIh/WIgLPyJi\nBBEXfkTECGK4Or5Ih5ve52tLZyjVsasbK6jOzK64rKsDQJYIJZvOXJPi37hCiysMmmTe2921emCT\nCDBFiJzRcbRvb6tePD5hTXaVkrriZipWT/va86qPPvjAd3XKb3vE7mV843nNx/d3f2VvYXpW3Vxn\niE/y0lWbp69JEWc1F6l2cVnJQloJpwa35jzOM1B3LsE7RNLZEh0jc+wDwLmlJe1/3Lo3l2t6LwrE\n9e/12VpJv1vBk5ZQJN/KJb2fpVLvnAk+wu+WpHyQHmXghkyCB9XpPeIbPyJiBBEXfkTECGKoor6I\ndFJUFcas+Jp1hBUG5DkViE0hOA44mLTQjjeNRHMW3Tz3WsgRF32w4mtSVZF4ZVVNTZmc/S7zR9S8\nl8tbcolmi1JcW4c5LC8rX2mVUj89PzFpG5IZLQlTpmp6gX7Lc1p+7vlnTTsmLWk5WbNGpi1OG15w\nKliZCEd2XaqwCxeWOuWFO9Scl0rbPr761F93yvVg30MFUpPmiOt/enbetJssHuuUK8402aQ0X6m0\nPu4+mrBFUYg+PDSp7//seNys+D1MxDd+RMQIIi78iIgRxNBF/WybijrjiDJSFLzSdFx37C7FxBAt\n2HY1olLOZq3qwAE8TNgxPmFFZQ7maTZtcAw78uXIQ0xcNtV18nzLukCiFFkeJGvnYHtdd/yXzr2s\nY6pY68LctHq45TP2t7teVq+240dVPG45GZX58ryXY57GVSDq8NCw81HMa7tKzeotF86d0f5TOge5\nglWL1jfUQlFzloEiBUItzCm1+ZhLWcbEITub1qtvZ0fnbpPSnjUdj2E+3zvnq/Uy9Vme9z+nS+o3\nx7c+wYR6vkYijoiIiB6ICz8iYgQRF35ExAhiuDp+KkXmLcdn3yT+9qZVnJKmDrNA6lHTpYjmaLGs\n417nvYEs6cVM7AEAddLBV1ZsZF1COm7+kkaL+TTZ0zNqXhLn7cZttzetN936uuq7G1uqq1Z3XfTc\nmu4FFNN2ro5O6vWuBiIfSex+CHvhFYt2DiYpzTdHgVXLdq+BU3s57hTUSYdeuaSegNNHbFLlhUXl\n3OfvD9i05BvrK51y3uUSKO/SPDpi+ZkF/S7bZZ3HbN7urwiZbms+zwBdzkeVMte9sS57vo7A5Zs3\n+3lu/oNi4Dd+O1X210Tks+3je0TkKRE5LSJ/ICK9d0ciIiJeUTiIqP+zAJ6n418B8GshhPsAbAB4\n7FYOLCIi4vZhIFFfRE4C+CEA/xXAv5M9OePdAH6i3eTjAH4RwG9dv7c9MSdp9TbZccAOYAMoWEhq\nNqwJKUsmwpQzmXAfzNWXzViVoElmL+nim9c6NjkyFz8ATE+oiF133n9jlEXWi43nz367U15bU7F3\nbv6oadds6ZjrzqS5uqXX3lxST0Dx6a9I9SlO2Ay2M9N6nJAK1mxaj7lqTT38pmasd2GWSFLKFBAz\nPWMDcWaO3kVjsl6OgM7d5KR68dXcfc+R9+Xqqs3W3iQijl0i3/AmTL63XhRn4gwvYbda7C1K/TlV\nlq2pvUyAw8Sgb/xfB/ALUM1lHsBmCJ2nehnAHfudGBER8crDdRe+iPwwgNUQwleu17bH+Y+LyNMi\n8rTftIuIiDgcDCLqvwPAj4jIDwIoAJgC8BsAZkQk037rnwRwYb+TQwhPAHgCALL53KsniiEi4h8w\nrrvwQwgfAfARABCRdwL49yGEnxSRPwTwowA+AeCDAD593auFgOQa0UWfnwBnAettuvD6FpU9EQep\ni8iQu61P/cxdpt1AUimdrjyRdzYc732ZovimJi2BZIUi2lYu29/KOvPbG1OlHeMdd2q02/y81bvL\n20T0UdAIws0dS7bBPc4uHDN1U1OqT7MLc7FgCTXXrmjOuu2S3ed44+s0R0BpR81oC0dPmHaTFGnn\n3YpLRITCexJ8HwBg/Sp9zzWXS5DMmJvkEp0Vn05b577loz77wOj1gSMe7cOZou/W8vsLhxDVdzMO\nPB/C3kbfaezp/B+9NUOKiIi43TiQA08I4QsAvtAunwHw1ls/pIiIiNuNoXruhRDUDOakG05X5UWt\nOpmN0v28qAJ7UVkzGp/HvHotFyWYI0IQ5vMHgEZtf+71Ws16eq1fVS+zhktPNTOrnmTNuhWPmyRW\ncxrnCWduy5DZyxNDZPM65ukFndPSM18z7caJw27SqSMLi3d2yvmCjuPSeZu6ij0n6y4VWUImt6kZ\n/c5w9zZNsvK8y0/QID77KuUxCM5EeuaMmkF3d603JKtPLZrvQtY+OzVKjdVtzuvtJcdtrYefa2dy\nbfeO8DuAlnFTiL76EREjiLjwIyJGEENPoXWNtKLbc0+Pxf0cJSTaNUhm93TPhvI6a78a03KnSdQK\nbhwh6HmepKNCnl8mg61PB0Y70DsusCVbVFE84/j4isQxN0/eehPT1tuNzR4t/9tN37NMRBZeWK2U\n1ZvuylVrXbjrHrUaTEypmtFIXjLtdksqfs/MWHVhfka/S66ofWQc+UiWiD7K23au2PttdVWz7G5t\nrJl2q5e1Lp11FOA0PfxI+CzJLGKLn1OavMHVgMHVBZbuDeXHLeH13h/xjR8RMYKICz8iYgQRF35E\nxAhi+Dp+W0fyunWDzG+ebDOX12g05svPuBRavDeQdvYUwx1P/Oo+FXaTTHZeM+a0XxX2zpt1Ojj9\nnpZdqqZ6bUmv7Ww3eTIlFsZ0f2Fq1kbnZSktdHC6Y4rmhAlBFxetd96FZTXNlbeszlwljvyEdOGi\n05+np3SMmZwlI6lVyfSZ0jlImrbdDrXbWLti6tavqFmUyTa2ty1hR4v2h1LOLS5HYw6U0yDxW0xU\n9ntMDK+rs87f3wGvX6XZRNi3765jf98PSMwR3/gRESOIuPAjIkYQwxX1Q0DS5mJrOVkrGLHaisAs\n3ufJ/JNzhB0s7XgyDxbvmUfOC2DM85ZznPhT84udcmVXxddyyQbA1Gt63HCZV9mla3raBtiwOa9O\nnm8pl+6Jg0FS7re7RubDEvHIH120dAkbxG931933mrppQ8Sh9+I197/OtLu8qvkDzl2wXn11SsNV\npRRUVeflmNAN8EE6u9vKO8iifnHMcgSyubNesapVVvQ5290hj7+Uy6bcJ5stm9W8asgPUOhR3js2\nyoSp42CwJj1/XU58oZ9J8GCmv/jGj4gYQcSFHxExgogLPyJiBHFo0XneZMfElj7FdY5MRRzFJ85V\nlvOhpV30VYGJOOm8xHHzJxQhV/B59RqqR7GuWnUmO8O/79J/J7S3Udm1+u7ElOrnp+5/sFMubduI\nszwRYlS2nU7LLs2kJbaceXNyQskwH3jDQ6buPtLlr6ypnr14xO5JbFCeuhWKSASAWTJxnj+71Clf\nvmj3AtiF2c/32JjOXWmX3KB3bJ4B5sgXx6u/Q2bXGrlZJ4l//jiXoJ0roWNfx0QuTP4SumjmtP+0\ny3fY4DTcfUg/jRrvVfoDvsLjGz8iYgQRF35ExAhi6J5717zVvBiTItklle4t6jNBhefEY7Hdp0FO\nUmomYZ50P440pdBquT5qbLZj0TBnpzGX4ug/2wfnAqhVLUmHEEf+6rKmmW5UrOfeFKXJrmyv22tT\nCNqReRW3PWnJ1oaa7LpINBIVUzki8bwzlW1uqQrCJkAAmJxQEZ7noNGomnbplqot4kxlubTOY62i\n3oTMaQgAY6Im3rSTgUslvV7CabidpxtzYzThU7Pxgakyzws/p/75a9C16zVb582Yva7VDwfl6o9v\n/IiIEURc+BERI4jh7upDxaaU22VO0657zu2Ep0l8bVJgS85lxC3Qec2ujLvkEUWiVtYFl7Don07b\n6Rmj61UrWpcem7DtKDDk6poLKKFyJmeDjDgl1caaUka72BgUaBd7a9MG2ISErBKkgpw4YT33OEjq\nueeeMXWbZCloEJlHyakmZ8682CnzDjwA1Gn+t8nLMTNmeQxnF1SNEWfp2dpSNSNDz8fEhPXcY7G6\n5NKZ9dox7/LOGzTZixO/k+b+qlt3MA+XXSep/WV66fL+2z+Y50YQ3/gRESOIuPAjIkYQceFHRIwg\nhm7OuwavAwmb87znFHnrsZrjvf+yZFqB416vMcEG2T4yjlef9UVPyMieX+ytV3VpmzGpOv8UpXcG\ngEaB9iEadvycVNTmGbDt+Nqe0CRNRBwmHsyRlkxMqUnwa9+wnPvrm+oZl6M53diyHnMXLylJ5yNv\ne4ep26K2nNY6caYrvreVijX1be2oCS9NezFTRavjs8mx1fRzquUacez7PaAbxqC6NtPqu/0F6cH8\n0U22OSjpx/Ux0MIXkSUAOwCaAJIQwsMiMgfgDwCcArAE4AMhhI1efURERLxycBBR/10hhIdCCA+3\njz8M4MkQwv0AnmwfR0REvApwM6L++wG8s13+OPZy6n2o3wkCFXO8SYP553z6K+bcz2VVzGslVsSu\nkcdZw4l8FSKoyBOfvecqM6NynHiFgprziPYO1abNlru9rdfOe5PjmF47m7ZkIdvbKh5nyItPGjaY\nJ9VSkbjh1IwWic4bG+pZNz65bdrdd9/rO+WLF5dN3RqRdKTIpsReagDw+je8oVOecxl3d0kdWTim\nKbm2tqxQuEumvokJa+rL0LV3tnX8lZr3eCQVyY0xP0Z8jeTpWXepzRJS8fplr+3mx9+fHKMfj/6g\n8EFohgTE2/raVYOqAIO+8QOAvxSRr4jI4+3PFkMI1yhYLgNY3P/UiIiIVxoGfeM/GkK4ICJHAXxO\nRL7FlSGEIOJ/gvbQ/qF4fK98U2ONiIi4RRjojR9CuND+vwrgU9hLj70iIscBoP1/tce5T4QQHm5v\nCN6aUUdERNwUrvvGF5FxAKkQwk67/P0A/jOAzwD4IIBfbv//9EBXbC9+T7aRJ5fPfMHqxax5N4iM\nEE0XVUZ6W5cpjvjbi+Ri612H2TxWr1vdnX8mjRnQmYbKJdVHd90+wcSkkk1knS8uX3unqtduuGg0\nJgQdcym00xS9WKHxb2xZHX+GCCofffQ9pu7ckubIO31Gy9ms3TcpUhrxmp9vo0PrD342Y+/t0eMn\nO2WfO6/e1Alv0uT7fAQc8Sf1fqnTOaW1ve85cp/2/feMnnOwQq9/ybEpbtAXoDN99thPAIBwze23\n2bOJwSCi/iKAT7Xf1hkAvxdC+HMR+TKAT4rIYwDOAvjAYJeMiIg4bFx34YcQzgB40z6frwF4T/cZ\nERERr3QMP4XWNVHfibljRRW/xxxvupA43iQTXiux4iWbaJrO1JfJMFeffu493ziKL+ei5zgaMGM4\n/KzYyKQXzcSKjRWKHstkLcdcgb53i/oPTqXZKmkfPjKQcwFMUYqrskvXvbyinPjjLrKuQmpRk0yJ\nItb8uE6ce5l80dTt7Or1VlY10hBuvjlt9rbzDFynyMMsRUpmncmukNc58KQi1mzHJmPHuUdStCct\nYbNalwDPKa84X0Mfvrx+5kJzXXe1QbbIwoDsHdFXPyJiBBEXfkTECCIu/IiIEcRwdXyRDkllxhFl\nMgOPOFPfGLnYGs76MatXZkjXDi2rj3IuusQQIVqdiFNLhy4dq1d+P0ccSs1yebtPkKXvWSvbaLTd\nRN1X0yk2gZlmyDPPe8bq58zzznnvvA8Fz+Omy2e3SumqeQ5KZUu2OU5Rcbtly3xTLqsJskrmyCNH\nT5h2nCMg7Nj+j53UnH5XiI8/uKxyu2UdfzplJ4v3X6yZzuvCQu2cGY3mzufO62Wa686dx+WDR/T5\ncfQ+J+r4ERERPRAXfkTECGLo5rxropH33GNZqOnSGxk+dELLiVlMnJk4U1+rpsdM4CFO5SgU1KS2\n41JjIadqwASle9p2Ka6YzKPZ8uY8jqyz34slOfYsq7sxZsl8lXjzFXkNssffxIzl5i9dUQ9rTj0O\nWNG5Rmm+PXd7q6VjXCXzIACsXdHjJn3PC8tLpl2tqnWeOHRiUslCJsnTcHfbEphm6X5Wq1ZtYXmZ\nxf7QJbL3I7lgjz8XMdcj5ZUX5wc24fUR57nuZt3f4xs/ImIEERd+RMQIYuii/jWvKE6FBdh0WF6K\nYb68LG1xO2XBiGhePeA+W5Rqy6fJSpGHWHDef5xJl0WtjPMkYzGyUbeiOGdUzbisqcwDx6JhsWi9\n8/LG282m0BojPro0EZisrV407XiHPp+3npJp8nLk+eZAJwBYuax9etWqXqfUVTTHBceXV6c+ExcU\ntbaq6gJbSlqt3mJuV1o1unaSEK+j87bkHf9+YnqXiE1NW/1ybRmvPlfFH/CufMo36z2Oa8eDKgDx\njR8RMYKICz8iYgQRF35ExAhiqDp+SlIotvPbeRJK9lTr1r/YvEcmDZ+CjOp8/xVK8cxeg56wI5fi\nqDurMVXIPJZN6xizrl2G6upukGnjSWbHn6H9hfFxq9czLl5Q3TeTs3slMzOq01YounB3x0a+MXdI\nNWd16zxFTuZoH2Ji3Jr9INquVvfeizr/OzTHpR0bJcj6bVc+hbTO69qVlU55htKEA0CdTLU+xXqg\nfQ7WkZPEp8LubYrr1Q6wujY/LwfivTc58fha/a/daxyDIL7xIyJGEHHhR0SMIIYcpAO0eogkDRK9\n0l3BMfz7RBxqLk2WCcFwcrQX2zvneHmbrp126bVSTTbFqYhdcOa2MpNtZKwq0aC0WRlHRuIDTK7B\nE1Qw2QKbJvfGrH0wF33VmcomSJWYXThi6opFDZxpUjBPccISh/QzgV2+rOQbjXU1OXrvP+NN525R\nilSmBnEQbm9b/sAipc0ulyw/IT87TZor/zwMYirbD9abztS4/rXsn7kgYd92XWmy+TQ/pPbXHFTD\niG/8iIgRRFz4EREjiLjwIyJGEMMn22zrdL0dGrsj2tgExrz6njAxT6athnMhzeU1cs+kUva580Jv\n8ooW69a0o1AoWEKQLLnUhrL9puzey66xe9cm0guKDGw401M+r9/TE5PyV9smLv2MY/PIEblJ2qXQ\nZn7QTE7bNZ2rLLsY7zozXZWIOLidTw3Oenw2Z8fIujATrtZdvsBsQ+fDk7PUyHU4TffTk6xmzL3o\nzYnfD+Zx8Z695pG2973FZPgc7ee3n1J9xnHAvNnxjR8RMYKICz8iYgQxVFE/BBWzfZriApFBiDd3\nkPeVUH7qLv5z4Qi/3nU5El8zzmTHImXW1TVYbKR03SkXnZcjUT/n6ozI6jj3ecwJyew+lTeLwBNT\n1ovt6op6uCVMaOLmqlxRUdxzsTM5yeSEmv2yOatysCqxvWXJSErkKWjyDLhrMelKxon6g3rF8TyO\njbtcBePzei2Oyqxbs19o0LFTA1J9zHTd5uBrY/RupWQudFX8PY1J0zU0on/K113LP7/vcLow0Btf\nRGZE5I9E5Fsi8ryIvE1E5kTkcyLyYvv/7PV7ioiIeCVgUFH/NwD8eQjhddhLp/U8gA8DeDKEcD+A\nJ9vHERERrwIMki13GsD3AviXABBCqAOoi8j7Abyz3ezjAL4A4EP9ewud4Ih02l06xaK4DbARkl+Y\naMGL4izK+R1iFpOMNcAFhnDwRtN5xfHudIV46by6kCPevnzeipSVKqk4XmSl3WoWFVNpK17y/NQd\nxxyn6OILJHX7Xao0/uDopFv0PYv0XWpOPF4j3j4ffMOek8yv6IkymHewUbPqH+/4Mzz9uhAHYXry\nmKkbm1jQMdGcNqrW+69e0u+S7FpOP6MWdG21h31K/SFOhO/pVdpFCNJ7GAel4BvkjX8PgCsAfltE\nviYi/72dLnsxhHAtTOwy9rLqRkREvAowyMLPAHgLgN8KIbwZQAlOrA97P6X7/uCJyOMi8rSIPN1r\nIyQiImK4GGThLwNYDiE81T7+I+z9EKyIyHEAaP9f3e/kEMITIYSHQwgP+zj7iIiIw8F1dfwQwmUR\nOS8irw0hfBvAewA81/77IIBfbv//9CAXFNl/8TfJ067q6lgnygUiynD7BMb7Sqwe2CQyiDSNwe81\npEmv3Nm2vPpsduGoNU/qwFa6lPOKawbSrZ2MxBIRq32eXIKj+jYpVXW7133H681LrOPXqjZyr2U8\n8nQOfNpwJjHx6cBNFCXtqUgf7zOv0zJTiYmCSzui1jE1KOUnj5u68VnV+TndWL3qPA131OxXzZ03\ndfVtJRVtlq3ZstXaP+dDX5Xbm5p7VEmfCEIvXw+clquNQe34/xbA78pegvQzAP4V9qSFT4rIYwDO\nAvjAga4cERFxaBho4YcQvg7g4X2q3nNrhxMRETEMDD1Ip2OH6DJhMLmEDbBhWSgQAQanwgJc5lLv\nOEWiP5NVBGeyqxP3ujfnMSccexA2nZSbo1Re9Yw1TTKvXuKIRHgLhL31Mi4HgeGOcwErg4IDobo9\nJbXM6odP12W9I/uJmr0DT4x3Xh8CDPZ4RM5mCM6MTXbK+aL1IxubVJKRLJkm63XbLlNQD8h0zgb6\nsJdmJbVk6sKuZhb2Hn8M6TM/7DnJmnCqD5mHN8EObEvs9B0RETFyiAs/ImIEERd+RMQIYsjReQGt\ntpLnVRLjtuhMfqz7sTUoNL1OpV8nm7d6cYPIJltN0uNTto8G5ctrOP05Jdp/Lq+6u7O2IUlovM5c\naFM1e452akfnedfVOrm2eoJKsx/Sz8TT2zI0MA5qQtoPbLIS5+dhTFtMYFKwEXiZgur4aa//F9Sd\nN5dX3T2dte2CqKnSm5xTlGshuAmvkDmvWSJX3y6mGb4xvR3ZbCCgn49Wj4YHvxfxjR8RMYKICz8i\nYgQht0JcG/hiIlew5+yzAODqdZrfbrwSxgDEcXjEcVgcdBx3hxCOXK/RUBd+56IiT4cQ9nMIGqkx\nxHHEcRzWOKKoHxExgogLPyJiBHFYC/+JQ7ou45UwBiCOwyOOw+K2jONQdPyIiIjDRRT1IyJGEENd\n+CLyPhH5toicFpGhsfKKyMdEZFVEnqHPhk4PLiJ3isjnReQ5EXlWRH72MMYiIgUR+ZKIfKM9jl9q\nf36PiDzVvj9/0OZfuO0QkXSbz/GzhzUOEVkSkb8Xka+LyNPtzw7jGRkKlf3QFr7sZbT4TQA/AOAB\nAD8uIg8M6fK/A+B97rPDoAdPAPx8COEBAI8A+Jn2HAx7LDUA7w4hvAnAQwDeJyKPAPgVAL8WQrgP\nwAaAx27zOK7hZ7FH2X4NhzWOd4UQHiLz2WE8I8Ohsg8hDOUPwNsA/AUdfwTAR4Z4/VMAnqHjbwM4\n3i4fB/DtYY2FxvBpAO89zLEAKAL4KoDvwZ6jSGa/+3Ubr3+y/TC/G8BnseeFfhjjWAKw4D4b6n0B\nMA3gZbT33m7nOIYp6t8BgMnMltufHRYOlR5cRE4BeDOApw5jLG3x+uvYI0n9HICXAGyG0GEHGdb9\n+XUAvwB00g/PH9I4AoC/FJGviMjj7c+GfV+GRmUfN/fQnx78dkBEJgD8MYCfCyGYzA7DGksIoRlC\neAh7b9y3Anjd7b6mh4j8MIDVEMJXhn3tffBoCOEt2FNFf0ZEvpcrh3RfborK/iAY5sK/AOBOOj7Z\n/uywMBA9+K2GiGSxt+h/N4TwJ4c5FgAIIWwC+Dz2ROoZkU7s8TDuzzsA/IiILAH4BPbE/d84hHEg\nhHCh/X8VwKew92M47PtyU1T2B8EwF/6XAdzf3rHNAfgxAJ8Z4vU9PoM9WnDgAPTgNwPZI5H7KIDn\nQwi/elhjEZEjIjLTLo9hb5/heez9APzosMYRQvhICOFkCOEU9p6H/xNC+Mlhj0NExkVk8loZwPcD\neAZDvi8hhMsAzovIa9sfXaOyv/XjuN2bJm6T4gcBvIA9ffI/DvG6vw/gEoAG9n5VH8OeLvkkgBcB\n/G8Ac0MYx6PYE9O+CeDr7b8fHPZYAHwngK+1x/EMgP/U/vw1AL4E4DSAPwSQH+I9eieAzx7GONrX\n+0b779lrz+YhPSMPAXi6fW/+F4DZ2zGO6LkXETGCiJt7EREjiLjwIyJGEHHhR0SMIOLCj4gYQcSF\nHxExgogLPyJiBBEXfkTECCIu/IiIEcT/BzXEcHTGyJuLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f4e9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example of a picture\n",
    "index = 25\n",
    "plt.imshow(train_set_x_orig[index])\n",
    "print (\"y = \" + str(train_set_y[:, index]) + \", it's a '\" + classes[np.squeeze(train_set_y[:, index])].decode(\"utf-8\") +  \"' picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many software bugs in deep learning come from having matrix/vector dimensions that don't fit. If you can keep your matrix/vector dimensions straight you will go a long way toward eliminating many bugs. \n",
    "\n",
    "**Exercise:** Find the values for:\n",
    "    - m_train (number of training examples)\n",
    "    - m_test (number of test examples)\n",
    "    - num_px (= height = width of a training image)\n",
    "Remember that `train_set_x_orig` is a numpy-array of shape (m_train, num_px, num_px, 3). For instance, you can access `m_train` by writing `train_set_x_orig.shape[0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training examples: m_train = 209\n",
      "Number of testing examples: m_test = 50\n",
      "Height/Width of each image: num_px = 64\n",
      "Each image is of size: (64, 64, 3)\n",
      "train_set_x shape: (209, 64, 64, 3)\n",
      "train_set_y shape: (1, 209)\n",
      "test_set_x shape: (50, 64, 64, 3)\n",
      "test_set_y shape: (1, 50)\n"
     ]
    }
   ],
   "source": [
    "### START CODE HERE ### (≈ 3 lines of code)\n",
    "m_train = train_set_x_orig.shape[0]\n",
    "m_test = test_set_x_orig.shape[0]\n",
    "num_px = train_set_x_orig.shape[1]\n",
    "### END CODE HERE ###\n",
    "\n",
    "print (\"Number of training examples: m_train = \" + str(m_train))\n",
    "print (\"Number of testing examples: m_test = \" + str(m_test))\n",
    "print (\"Height/Width of each image: num_px = \" + str(num_px))\n",
    "print (\"Each image is of size: (\" + str(num_px) + \", \" + str(num_px) + \", 3)\")\n",
    "print (\"train_set_x shape: \" + str(train_set_x_orig.shape))\n",
    "print (\"train_set_y shape: \" + str(train_set_y.shape))\n",
    "print (\"test_set_x shape: \" + str(test_set_x_orig.shape))\n",
    "print (\"test_set_y shape: \" + str(test_set_y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output for m_train, m_test and num_px**: \n",
    "<table style=\"width:15%\">\n",
    "  <tr>\n",
    "    <td>**m_train**</td>\n",
    "    <td> 209 </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**m_test**</td>\n",
    "    <td> 50 </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**num_px**</td>\n",
    "    <td> 64 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, you should now reshape images of shape (num_px, num_px, 3) in a numpy-array of shape (num_px $*$ num_px $*$ 3, 1). After this, our training (and test) dataset is a numpy-array where each column represents a flattened image. There should be m_train (respectively m_test) columns.\n",
    "\n",
    "**Exercise:** Reshape the training and test data sets so that images of size (num_px, num_px, 3) are flattened into single vectors of shape (num\\_px $*$ num\\_px $*$ 3, 1).\n",
    "\n",
    "A trick when you want to flatten a matrix X of shape (a,b,c,d) to a matrix X_flatten of shape (b$*$c$*$d, a) is to use: \n",
    "```python\n",
    "X_flatten = X.reshape(X.shape[0], -1).T      # X.T is the transpose of X\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_set_x_flatten shape: (12288, 209)\n",
      "train_set_y shape: (1, 209)\n",
      "test_set_x_flatten shape: (12288, 50)\n",
      "test_set_y shape: (1, 50)\n",
      "sanity check after reshaping: [17 31 56 22 33]\n"
     ]
    }
   ],
   "source": [
    "# Reshape the training and test examples\n",
    "\n",
    "### START CODE HERE ### (≈ 2 lines of code)\n",
    "train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T\n",
    "test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T\n",
    "### END CODE HERE ###\n",
    "\n",
    "print (\"train_set_x_flatten shape: \" + str(train_set_x_flatten.shape))\n",
    "print (\"train_set_y shape: \" + str(train_set_y.shape))\n",
    "print (\"test_set_x_flatten shape: \" + str(test_set_x_flatten.shape))\n",
    "print (\"test_set_y shape: \" + str(test_set_y.shape))\n",
    "print (\"sanity check after reshaping: \" + str(train_set_x_flatten[0:5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:35%\">\n",
    "  <tr>\n",
    "    <td>**train_set_x_flatten shape**</td>\n",
    "    <td> (12288, 209)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**train_set_y shape**</td>\n",
    "    <td>(1, 209)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**test_set_x_flatten shape**</td>\n",
    "    <td>(12288, 50)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**test_set_y shape**</td>\n",
    "    <td>(1, 50)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "  <td>**sanity check after reshaping**</td>\n",
    "  <td>[17 31 56 22 33]</td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To represent color images, the red, green and blue channels (RGB) must be specified for each pixel, and so the pixel value is actually a vector of three numbers ranging from 0 to 255.\n",
    "\n",
    "One common preprocessing step in machine learning is to center and standardize your dataset, meaning that you substract the mean of the whole numpy array from each example, and then divide each example by the standard deviation of the whole numpy array. But for picture datasets, it is simpler and more convenient and works almost as well to just divide every row of the dataset by 255 (the maximum value of a pixel channel).\n",
    "\n",
    "<!-- During the training of your model, you're going to multiply weights and add biases to some initial inputs in order to observe neuron activations. Then you backpropogate with the gradients to train the model. But, it is extremely important for each feature to have a similar range such that our gradients don't explode. You will see that more in detail later in the lectures. !--> \n",
    "\n",
    "Let's standardize our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_set_x = train_set_x_flatten/255.\n",
    "test_set_x = test_set_x_flatten/255."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you need to remember:**\n",
    "\n",
    "Common steps for pre-processing a new dataset are:\n",
    "- Figure out the dimensions and shapes of the problem (m_train, m_test, num_px, ...)\n",
    "- Reshape the datasets such that each example is now a vector of size (num_px \\* num_px \\* 3, 1)\n",
    "- \"Standardize\" the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - General Architecture of the learning algorithm ##\n",
    "\n",
    "It's time to design a simple algorithm to distinguish cat images from non-cat images.\n",
    "\n",
    "You will build a Logistic Regression, using a Neural Network mindset. The following Figure explains why **Logistic Regression is actually a very simple Neural Network!**\n",
    "\n",
    "<img src=\"images/LogReg_kiank.png\" style=\"width:650px;height:400px;\">\n",
    "\n",
    "**Mathematical expression of the algorithm**:\n",
    "\n",
    "For one example $x^{(i)}$:\n",
    "$$z^{(i)} = w^T x^{(i)} + b \\tag{1}$$\n",
    "$$\\hat{y}^{(i)} = a^{(i)} = sigmoid(z^{(i)})\\tag{2}$$ \n",
    "$$ \\mathcal{L}(a^{(i)}, y^{(i)}) =  - y^{(i)}  \\log(a^{(i)}) - (1-y^{(i)} )  \\log(1-a^{(i)})\\tag{3}$$\n",
    "\n",
    "The cost is then computed by summing over all training examples:\n",
    "$$ J = \\frac{1}{m} \\sum_{i=1}^m \\mathcal{L}(a^{(i)}, y^{(i)})\\tag{6}$$\n",
    "\n",
    "**Key steps**:\n",
    "In this exercise, you will carry out the following steps: \n",
    "    - Initialize the parameters of the model\n",
    "    - Learn the parameters for the model by minimizing the cost  \n",
    "    - Use the learned parameters to make predictions (on the test set)\n",
    "    - Analyse the results and conclude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Building the parts of our algorithm ## \n",
    "\n",
    "The main steps for building a Neural Network are:\n",
    "1. Define the model structure (such as number of input features) \n",
    "2. Initialize the model's parameters\n",
    "3. Loop:\n",
    "    - Calculate current loss (forward propagation)\n",
    "    - Calculate current gradient (backward propagation)\n",
    "    - Update parameters (gradient descent)\n",
    "\n",
    "You often build 1-3 separately and integrate them into one function we call `model()`.\n",
    "\n",
    "### 4.1 - Helper functions\n",
    "\n",
    "**Exercise**: Using your code from \"Python Basics\", implement `sigmoid()`. As you've seen in the figure above, you need to compute $sigmoid( w^T x + b) = \\frac{1}{1 + e^{-(w^T x + b)}}$ to make predictions. Use np.exp()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: sigmoid\n",
    "\n",
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    Compute the sigmoid of z\n",
    "\n",
    "    Arguments:\n",
    "    z -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(z)\n",
    "    \"\"\"\n",
    "\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    s = 1/(1 + np.exp(-z))\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigmoid([0, 2]) = [ 0.5         0.88079708]\n"
     ]
    }
   ],
   "source": [
    "print (\"sigmoid([0, 2]) = \" + str(sigmoid(np.array([0,2]))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <td>**sigmoid([0, 2])**</td>\n",
    "    <td> [ 0.5         0.88079708]</td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 - Initializing parameters\n",
    "\n",
    "**Exercise:** Implement parameter initialization in the cell below. You have to initialize w as a vector of zeros. If you don't know what numpy function to use, look up np.zeros() in the Numpy library's documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_with_zeros\n",
    "\n",
    "def initialize_with_zeros(dim):\n",
    "    \"\"\"\n",
    "    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.\n",
    "    \n",
    "    Argument:\n",
    "    dim -- size of the w vector we want (or number of parameters in this case)\n",
    "    \n",
    "    Returns:\n",
    "    w -- initialized vector of shape (dim, 1)\n",
    "    b -- initialized scalar (corresponds to the bias)\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    w = np.zeros([dim, 1])\n",
    "    b = 0\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(w.shape == (dim, 1))\n",
    "    assert(isinstance(b, float) or isinstance(b, int))\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.]\n",
      " [ 0.]]\n",
      "b = 0\n"
     ]
    }
   ],
   "source": [
    "dim = 2\n",
    "w, b = initialize_with_zeros(dim)\n",
    "print (\"w = \" + str(w))\n",
    "print (\"b = \" + str(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "\n",
    "<table style=\"width:15%\">\n",
    "    <tr>\n",
    "        <td>  ** w **  </td>\n",
    "        <td> [[ 0.]\n",
    " [ 0.]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** b **  </td>\n",
    "        <td> 0 </td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "For image inputs, w will be of shape (num_px $\\times$ num_px $\\times$ 3, 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 - Forward and Backward propagation\n",
    "\n",
    "Now that your parameters are initialized, you can do the \"forward\" and \"backward\" propagation steps for learning the parameters.\n",
    "\n",
    "**Exercise:** Implement a function `propagate()` that computes the cost function and its gradient.\n",
    "\n",
    "**Hints**:\n",
    "\n",
    "Forward Propagation:\n",
    "- You get X\n",
    "- You compute $A = \\sigma(w^T X + b) = (a^{(0)}, a^{(1)}, ..., a^{(m-1)}, a^{(m)})$\n",
    "- You calculate the cost function: $J = -\\frac{1}{m}\\sum_{i=1}^{m}y^{(i)}\\log(a^{(i)})+(1-y^{(i)})\\log(1-a^{(i)})$\n",
    "\n",
    "Here are the two formulas you will be using: \n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial w} = \\frac{1}{m}X(A-Y)^T\\tag{7}$$\n",
    "$$ \\frac{\\partial J}{\\partial b} = \\frac{1}{m} \\sum_{i=1}^m (a^{(i)}-y^{(i)})\\tag{8}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: propagate\n",
    "\n",
    "def propagate(w, b, X, Y):\n",
    "    \"\"\"\n",
    "    Implement the cost function and its gradient for the propagation explained above\n",
    "\n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)\n",
    "\n",
    "    Return:\n",
    "    cost -- negative log-likelihood cost for logistic regression\n",
    "    dw -- gradient of the loss with respect to w, thus same shape as w\n",
    "    db -- gradient of the loss with respect to b, thus same shape as b\n",
    "    \n",
    "    Tips:\n",
    "    - Write your code step by step for the propagation. np.log(), np.dot()\n",
    "    \"\"\"\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    \n",
    "    # FORWARD PROPAGATION (FROM X TO COST)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A = sigmoid(np.dot(w.T, X) + b)            # compute activation\n",
    "    cost = -(np.dot(Y, np.log(A).T) + np.dot((1-Y), np.log(1-A).T))/m         # compute cost\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # BACKWARD PROPAGATION (TO FIND GRAD)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    dw = np.dot(X, (A-Y).T) / m\n",
    "    db = np.sum(A - Y)/m\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(dw.shape == w.shape)\n",
    "    assert(db.dtype == float)\n",
    "    cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return grads, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dw = [[ 0.99993216]\n",
      " [ 1.99980262]]\n",
      "db = 0.499935230625\n",
      "cost = 6.000064773192205\n"
     ]
    }
   ],
   "source": [
    "w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])\n",
    "grads, cost = propagate(w, b, X, Y)\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))\n",
    "print (\"cost = \" + str(cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\">\n",
    "    <tr>\n",
    "        <td>  ** dw **  </td>\n",
    "        <td> [[ 0.99993216]\n",
    " [ 1.99980262]]</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** db **  </td>\n",
    "        <td> 0.499935230625 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** cost **  </td>\n",
    "        <td> 6.000064773192205</td>\n",
    "    </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Optimization\n",
    "- You have initialized your parameters.\n",
    "- You are also able to compute a cost function and its gradient.\n",
    "- Now, you want to update the parameters using gradient descent.\n",
    "\n",
    "**Exercise:** Write down the optimization function. The goal is to learn $w$ and $b$ by minimizing the cost function $J$. For a parameter $\\theta$, the update rule is $ \\theta = \\theta - \\alpha \\text{ } d\\theta$, where $\\alpha$ is the learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: optimize\n",
    "\n",
    "def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):\n",
    "    \"\"\"\n",
    "    This function optimizes w and b by running a gradient descent algorithm\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of shape (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    learning_rate -- learning rate of the gradient descent update rule\n",
    "    print_cost -- True to print the loss every 100 steps\n",
    "    \n",
    "    Returns:\n",
    "    params -- dictionary containing the weights w and bias b\n",
    "    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function\n",
    "    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.\n",
    "    \n",
    "    Tips:\n",
    "    You basically need to write down two steps and iterate through them:\n",
    "        1) Calculate the cost and the gradient for the current parameters. Use propagate().\n",
    "        2) Update the parameters using gradient descent rule for w and b.\n",
    "    \"\"\"\n",
    "    \n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        \n",
    "        \n",
    "        # Cost and gradient calculation (≈ 1-4 lines of code)\n",
    "        ### START CODE HERE ### \n",
    "        grads, cost = propagate(w, b, X, Y)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Retrieve derivatives from grads\n",
    "        dw = grads[\"dw\"]\n",
    "        db = grads[\"db\"]\n",
    "        \n",
    "        # update rule (≈ 2 lines of code)\n",
    "        ### START CODE HERE ###\n",
    "        w = w - learning_rate * dw\n",
    "        b = b - learning_rate * db\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Record the costs\n",
    "        if i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "        \n",
    "        # Print the cost every 100 training examples\n",
    "        if print_cost and i % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "    \n",
    "    params = {\"w\": w,\n",
    "              \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return params, grads, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.1124579 ]\n",
      " [ 0.23106775]]\n",
      "b = 1.55930492484\n",
      "dw = [[ 0.90158428]\n",
      " [ 1.76250842]]\n",
      "db = 0.430462071679\n"
     ]
    }
   ],
   "source": [
    "params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)\n",
    "\n",
    "print (\"w = \" + str(params[\"w\"]))\n",
    "print (\"b = \" + str(params[\"b\"]))\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\">\n",
    "    <tr>\n",
    "       <td> **w** </td>\n",
    "       <td>[[ 0.1124579 ]\n",
    " [ 0.23106775]] </td>\n",
    "    </tr>\n",
    "    \n",
    "    <tr>\n",
    "       <td> **b** </td>\n",
    "       <td> 1.55930492484 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **dw** </td>\n",
    "       <td> [[ 0.90158428]\n",
    " [ 1.76250842]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **db** </td>\n",
    "       <td> 0.430462071679 </td>\n",
    "    </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** The previous function will output the learned w and b. We are able to use w and b to predict the labels for a dataset X. Implement the `predict()` function. There is two steps to computing predictions:\n",
    "\n",
    "1. Calculate $\\hat{Y} = A = \\sigma(w^T X + b)$\n",
    "\n",
    "2. Convert the entries of a into 0 (if activation <= 0.5) or 1 (if activation > 0.5), stores the predictions in a vector `Y_prediction`. If you wish, you can use an `if`/`else` statement in a `for` loop (though there is also a way to vectorize this). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: predict\n",
    "\n",
    "def predict(w, b, X):\n",
    "    '''\n",
    "    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X\n",
    "    '''\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    Y_prediction = np.zeros((1,m))\n",
    "    w = w.reshape(X.shape[0], 1)\n",
    "    \n",
    "    # Compute vector \"A\" predicting the probabilities of a cat being present in the picture\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    A = sigmoid(np.dot(w.T, X) + b) \n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    for i in range(A.shape[1]):\n",
    "        \n",
    "        # Convert probabilities A[0,i] to actual predictions p[0,i]\n",
    "        ### START CODE HERE ### (≈ 4 lines of code)\n",
    "        Y_prediction[0, i] = A[0, i] > 0.5\n",
    "        ### END CODE HERE ###\n",
    "    \n",
    "    assert(Y_prediction.shape == (1, m))\n",
    "    \n",
    "    return Y_prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions = [[ 1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print (\"predictions = \" + str(predict(w, b, X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:30%\">\n",
    "    <tr>\n",
    "         <td>\n",
    "             **predictions**\n",
    "         </td>\n",
    "          <td>\n",
    "            [[ 1.  1.]]\n",
    "         </td>  \n",
    "   </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<font color='blue'>\n",
    "**What to remember:**\n",
    "You've implemented several functions that:\n",
    "- Initialize (w,b)\n",
    "- Optimize the loss iteratively to learn parameters (w,b):\n",
    "    - computing the cost and its gradient \n",
    "    - updating the parameters using gradient descent\n",
    "- Use the learned (w,b) to predict the labels for a given set of examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Merge all functions into a model ##\n",
    "\n",
    "You will now see how the overall model is structured by putting together all the building blocks (functions implemented in the previous parts) together, in the right order.\n",
    "\n",
    "**Exercise:** Implement the model function. Use the following notation:\n",
    "    - Y_prediction for your predictions on the test set\n",
    "    - Y_prediction_train for your predictions on the train set\n",
    "    - w, costs, grads for the outputs of optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: model\n",
    "\n",
    "def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):\n",
    "    \"\"\"\n",
    "    Builds the logistic regression model by calling the function you've implemented previously\n",
    "    \n",
    "    Arguments:\n",
    "    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)\n",
    "    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)\n",
    "    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)\n",
    "    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)\n",
    "    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters\n",
    "    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()\n",
    "    print_cost -- Set to true to print the cost every 100 iterations\n",
    "    \n",
    "    Returns:\n",
    "    d -- dictionary containing information about the model.\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ###\n",
    "    \n",
    "    # initialize parameters with zeros (≈ 1 line of code)\n",
    "    w, b = initialize_with_zeros(X_train.shape[0])\n",
    "\n",
    "    # Gradient descent (≈ 1 line of code)\n",
    "    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)\n",
    "    \n",
    "    # Retrieve parameters w and b from dictionary \"parameters\"\n",
    "    w = parameters['w']\n",
    "    b = parameters['b']\n",
    "    \n",
    "    # Predict test/train set examples (≈ 2 lines of code)\n",
    "    Y_prediction_test = predict(w, b, X_test)\n",
    "    Y_prediction_train = predict(w, b, X_train)\n",
    "\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    # Print train/test Errors\n",
    "    print(\"train accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))\n",
    "    print(\"test accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))\n",
    "\n",
    "    \n",
    "    d = {\"costs\": costs,\n",
    "         \"Y_prediction_test\": Y_prediction_test, \n",
    "         \"Y_prediction_train\" : Y_prediction_train, \n",
    "         \"w\" : w, \n",
    "         \"b\" : b,\n",
    "         \"learning_rate\" : learning_rate,\n",
    "         \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following cell to train your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693147\n",
      "Cost after iteration 100: 0.584508\n",
      "Cost after iteration 200: 0.466949\n",
      "Cost after iteration 300: 0.376007\n",
      "Cost after iteration 400: 0.331463\n",
      "Cost after iteration 500: 0.303273\n",
      "Cost after iteration 600: 0.279880\n",
      "Cost after iteration 700: 0.260042\n",
      "Cost after iteration 800: 0.242941\n",
      "Cost after iteration 900: 0.228004\n",
      "Cost after iteration 1000: 0.214820\n",
      "Cost after iteration 1100: 0.203078\n",
      "Cost after iteration 1200: 0.192544\n",
      "Cost after iteration 1300: 0.183033\n",
      "Cost after iteration 1400: 0.174399\n",
      "Cost after iteration 1500: 0.166521\n",
      "Cost after iteration 1600: 0.159305\n",
      "Cost after iteration 1700: 0.152667\n",
      "Cost after iteration 1800: 0.146542\n",
      "Cost after iteration 1900: 0.140872\n",
      "train accuracy: 99.04306220095694 %\n",
      "test accuracy: 70.0 %\n"
     ]
    }
   ],
   "source": [
    "d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    \n",
    "    <tr>\n",
    "        <td> **Train Accuracy**  </td> \n",
    "        <td> 99.04306220095694 % </td>\n",
    "    </tr>\n",
    "\n",
    "    <tr>\n",
    "        <td>**Test Accuracy** </td> \n",
    "        <td> 70.0 % </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Comment**: Training accuracy is close to 100%. This is a good sanity check: your model is working and has high enough capacity to fit the training data. Test error is 68%. It is actually not bad for this simple model, given the small dataset we used and that logistic regression is a linear classifier. But no worries, you'll build an even better classifier next week!\n",
    "\n",
    "Also, you see that the model is clearly overfitting the training data. Later in this specialization you will learn how to reduce overfitting, for example by using regularization. Using the code below (and changing the `index` variable) you can look at predictions on pictures of the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-20-50a2ff1ec91d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest_set_x\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_px\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_px\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mprint\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m\"y = \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest_set_y\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\", you predicted that it is a \\\"\"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mclasses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"Y_prediction_test\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdecode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"utf-8\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m  \u001b[0;34m\"\\\" picture.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m: only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices"
     ]
    },
    {
     "data": {
      "image/png": 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5M9GVO3A0iqAc2jejtltfiSZ8tqlt4AKVamtuxfNRN0lL+eHoxnVIdJMJb7X0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\nNz2kQ5PHJqJvmQ/6e+NDse/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UNoehqsH1ZkzdGLpNlymmtqHzcgUSw2xq7Xymr2z4qs3C\nS5qjChe2WYhNri2QPIZ0UY0QJUZCVJwR0dACphq8vlDvsq7B++rMQoxjZDLkI5v5cqivpfM4+69R\nj1l8ls4LXUKwu4mRSMJ29bqmcbUIKnQfmIJlmtWcbzofNkuwVnM6z+FwXAf+4DscA4i+mvoBoU15\nWM0wpqE6zDBFG/WYf9RRhyuamyHQYQf725fgEsBq0fE3kmnFbmIbIWg3gMt+q2ix7oJt5uPuZmlX\nHTl7vhOEPuw00l3MdDVGArUHaFPfRuTVq7FMttIXMdvxcXK0HwDk89H0Xy/HTL1mFzerm6m/C9fM\nM0kcgyM4LYWspBfJRe2IEqR51Iypf0si90RkQkT+UEReEpEXReQ9IjIlIt8QkVdb/3tFTIfjLYJe\nTf3fBvDnIYR7sF1O60UAnwbwZAjhBIAnW58dDsdbAL1Uyx0H8KMA/gUAhBCqAKoi8hEAj7U2+wKA\nbwP4VLexQghtEyVnTJKE9ez292I72WRVWmlmOx5fJVN0LEfzhtZs4hVzZQSrrZJW/zuGNPtO0R+6\nCU/0as6hS9KInlPyir82+21ZKD6A3la7O+bOx5ZKNuFrFYqANFWG+VxlM7qPqxWvr8S/29Jm7GZZ\nc17FfHaU0+J7jlVi9Fb1Gpvmet86qo/ZBb0VV8i1TEmlsj2mjWZNQi9v/OMArgL4XRH5noj811a5\n7LkQwqXWNpexXVXX4XC8BdDLg58B8DCA3wkhPARgE8asD9s/47v+1IjI4yJyUkROrqys7LaJw+Ho\nM3p58OcBzIcQnmp9/kNs/xBcEZEDAND6f2G3L4cQngghPBJCeGRiYuJmzNnhcNwgruvjhxAui8h5\nEbk7hPAygA8CeKH17+MAPtv6/yvXHwtotMr5Nho2Sos+dNa4VmO0NzPuVrOL/8+UmyjazNBtarc2\ncm/38kbWb20QlZjqEv3XKb2++++w/TtToQ0bTZfg43X6ptTXxT9nus1SsHxsdo6BaNJuevbd5phN\nU1lyGr9e1T5yJpdc4nqIfPxUKkbx1Wxpc0svE9Q57eZCJ0WHQkfd1cz8+fxLIR6LvZSckWdLs1da\nY/a6/tMrj/+vAfyeiOQAvAbgX2LbWviyiHwCwFkAH+1xLIfDscfo6cEPITwD4JFduj54c6fjcDj6\ngf5G7oWASn2blsnVtSBDlsKXrBadooPIVLSGcVC6+jZijtpdNOtV8dNukXtd9Nu4fFSn5ZWc8JG0\nr26CIJmUvoRWq7+X8S14f2oenSWO27BiIfy9bqY+R+F1RrvFpJo8mexZWz2Yxk+Zsmf5PLkL9L1a\nzVQx7hK5xxRZ2p42Zoa7ULDsl9rEKjUXHsNEldaIwqsYfcJKi+7s1OzfHR6r73AMIPzBdzgGEP7g\nOxwDiP77+C3fJF/VoZXKx88acUlFk5DvaNwZpts63VHO/iN/y1BZ6S40HWexpZToh91Xb358x7cS\n/O5uFJjFG9lf0n67htgmfs/WCKB1CBLH7CbKYcG+O5fCzufzel8ZXlMx6y1cf0/5+FtqO6bzup4P\nu/CTdLrtOpVKMLV172h9oRx994YZnDP8bA2CHTrvZobsOhyOf2DwB9/hGEBIz5leN2NnIlexHewz\nA+Ba33a8O94McwB8HhY+D403Oo9jIYTZ623U1we/vVORkyGE3QKCBmoOPg+fx17Nw019h2MA4Q++\nwzGA2KsH/4k92i/jzTAHwOdh4fPQuCXz2BMf3+Fw7C3c1Hc4BhB9ffBF5MMi8rKInBKRvqnyisjn\nRWRBRJ6jv/VdHlxEjojIt0TkBRF5XkQ+uRdzEZGCiPy9iDzbmsevtf5+XESeal2fL7X0F245RCTd\n0nP82l7NQ0TOiMgPROQZETnZ+tte3CN9kbLv24Mv28Xs/guAfwzgPgAfE5H7+rT7/wbgw+ZveyEP\nXgfwyyGE+wA8CuAXW+eg33OpAPhACOEBAA8C+LCIPArg1wH8ZgjhTgDLAD5xi+exg09iW7J9B3s1\njx8LITxI9Nle3CP9kbIPIfTlH4D3APg6ff4MgM/0cf+3AXiOPr8M4ECrfQDAy/2aC83hKwA+tJdz\nATAE4LsA3o3tQJHMbtfrFu7/cOtm/gCAr2E7+n0v5nEGwIz5W1+vC4BxAK+jtfZ2K+fRT1P/EIDz\n9Hm+9be9wp7Kg4vIbQAeAvDUXsylZV4/g22R1G8AOA1gJYSwk0XTr+vzWwB+BbGiwfQezSMA+AsR\n+Y6IPN76W7+vS9+k7H1xD93lwW8FRGQEwB8B+KUQwtpezCWE0AghPIjtN+67ANxzq/dpISI/DWAh\nhPCdfu97F7w/hPAwtl3RXxSRH+XOPl2XG5KyfyPo54N/AcAR+ny49be9Qk/y4DcbIpLF9kP/eyGE\nP97LuQBACGEFwLewbVJPiMhO7mo/rs/7APyMiJwB8EVsm/u/vQfzQAjhQuv/BQB/gu0fw35flxuS\nsn8j6OeD/zSAE60V2xyAnwPw1T7u3+Kr2JYFB3qUB79RyHay/OcAvBhC+I29mouIzIrIRKtdxPY6\nw4vY/gH42X7NI4TwmS92ZXwAAADgSURBVBDC4RDCbdi+H/4yhPAL/Z6HiAyLyOhOG8BPAHgOfb4u\nIYTLAM6LyN2tP+1I2d/8edzqRROzSPFTAF7Btj/57/u4398HcAnbRcvmsb1KPI3tRaVXAXwTwFQf\n5vF+bJtp3wfwTOvfT/V7LgDuB/C91jyeA/AfWn+/HcDfAzgF4A8A5Pt4jR4D8LW9mEdrf8+2/j2/\nc2/u0T3yIICTrWvzPwFM3op5eOSewzGA8MU9h2MA4Q++wzGA8Aff4RhA+IPvcAwg/MF3OAYQ/uA7\nHAMIf/AdjgGEP/gOxwDi/wMzltccK+P2RQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d63eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example of a picture that was wrongly classified.\n",
    "index = 1\n",
    "plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))\n",
    "print (\"y = \" + str(test_set_y[0,index]) + \", you predicted that it is a \\\"\" + classes[d[\"Y_prediction_test\"][0,index]].decode(\"utf-8\") +  \"\\\" picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also plot the cost function and the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113dd55c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot learning curve (with costs)\n",
    "costs = np.squeeze(d['costs'])\n",
    "plt.plot(costs)\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (per hundreds)')\n",
    "plt.title(\"Learning rate =\" + str(d[\"learning_rate\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Interpretation**:\n",
    "You can see the cost decreasing. It shows that the parameters are being learned. However, you see that you could train the model even more on the training set. Try to increase the number of iterations in the cell above and rerun the cells. You might see that the training set accuracy goes up, but the test set accuracy goes down. This is called overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 - Further analysis (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on building your first image classification model. Let's analyze it further, and examine possible choices for the learning rate $\\alpha$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Choice of learning rate ####\n",
    "\n",
    "**Reminder**:\n",
    "In order for Gradient Descent to work you must choose the learning rate wisely. The learning rate $\\alpha$  determines how rapidly we update the parameters. If the learning rate is too large we may \"overshoot\" the optimal value. Similarly, if it is too small we will need too many iterations to converge to the best values. That's why it is crucial to use a well-tuned learning rate.\n",
    "\n",
    "Let's compare the learning curve of our model with several choices of learning rates. Run the cell below. This should take about 1 minute. Feel free also to try different values than the three we have initialized the `learning_rates` variable to contain, and see what happens. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "learning rate is: 0.01\n",
      "train accuracy: 99.52153110047847 %\n",
      "test accuracy: 68.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.001\n",
      "train accuracy: 88.99521531100478 %\n",
      "test accuracy: 64.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.0001\n",
      "train accuracy: 68.42105263157895 %\n",
      "test accuracy: 36.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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qdNe/eH0zf/1wNxt+ej5Oh+awUqrv6XUKXeXKtM5IOrID/nkLHBOWdpuduWPmsuzSZczO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\naLWbo9X1HK2p94bF0WrPVOOmzLPui7J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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1149820f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rates = [0.01, 0.001, 0.0001]\n",
    "models = {}\n",
    "for i in learning_rates:\n",
    "    print (\"learning rate is: \" + str(i))\n",
    "    models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)\n",
    "    print ('\\n' + \"-------------------------------------------------------\" + '\\n')\n",
    "\n",
    "for i in learning_rates:\n",
    "    plt.plot(np.squeeze(models[str(i)][\"costs\"]), label= str(models[str(i)][\"learning_rate\"]))\n",
    "\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations')\n",
    "\n",
    "legend = plt.legend(loc='upper center', shadow=True)\n",
    "frame = legend.get_frame()\n",
    "frame.set_facecolor('0.90')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**: \n",
    "- Different learning rates give different costs and thus different predictions results.\n",
    "- If the learning rate is too large (0.01), the cost may oscillate up and down. It may even diverge (though in this example, using 0.01 still eventually ends up at a good value for the cost). \n",
    "- A lower cost doesn't mean a better model. You have to check if there is possibly overfitting. It happens when the training accuracy is a lot higher than the test accuracy.\n",
    "- In deep learning, we usually recommend that you: \n",
    "    - Choose the learning rate that better minimizes the cost function.\n",
    "    - If your model overfits, use other techniques to reduce overfitting. (We'll talk about this in later videos.) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 7 - Test with your own image (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on finishing this assignment. You can use your own image and see the output of your model. To do that:\n",
    "    1. Click on \"File\" in the upper bar of this notebook, then click \"Open\" to go on your Coursera Hub.\n",
    "    2. Add your image to this Jupyter Notebook's directory, in the \"images\" folder\n",
    "    3. Change your image's name in the following code\n",
    "    4. Run the code and check if the algorithm is right (1 = cat, 0 = non-cat)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/ipykernel_launcher.py:7: DeprecationWarning: `imread` is deprecated!\n",
      "`imread` is deprecated in SciPy 1.0.0.\n",
      "Use ``matplotlib.pyplot.imread`` instead.\n",
      "  import sys\n",
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/ipykernel_launcher.py:8: DeprecationWarning: `imresize` is deprecated!\n",
      "`imresize` is deprecated in SciPy 1.0.0, and will be removed in 1.2.0.\n",
      "Use ``skimage.transform.resize`` instead.\n",
      "  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 1.0, your algorithm predicts a \"cat\" picture.\n"
     ]
    },
    {
     "data": {
      "image/png": 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bVlRSWxMiFs1gFW0ofoW5hTEKU6fZvt2OrplYbD6MnIxaKKKoKuFiHsWm4Zbc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\nDA6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SJECQAElRtiRqlywvkmWNl7FsKzyeCY1X2WM/Wc9jS7ZkS5a1kqK4LyCJjViIHWh0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EIOhWBCddMym81RSvtJZI5sMkU5xe3bd9iut7zx2hskScLV1QW76w1XF094+Nxz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\nbPp3efLkyTTEHJ/8bdtzOOSy2u0MURJTVg3b3YHtfjel1xdFQVmW3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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11499ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## START CODE HERE ## (PUT YOUR IMAGE NAME) \n",
    "my_image = \"cat_in_iran.jpg\"   # change this to the name of your image file \n",
    "## END CODE HERE ##\n",
    "\n",
    "# We preprocess the image to fit your algorithm.\n",
    "fname = \"images/\" + my_image\n",
    "image = np.array(ndimage.imread(fname, flatten=False))\n",
    "my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T\n",
    "my_predicted_image = predict(d[\"w\"], d[\"b\"], my_image)\n",
    "\n",
    "plt.imshow(image)\n",
    "print(\"y = \" + str(np.squeeze(my_predicted_image)) + \", your algorithm predicts a \\\"\" + classes[int(np.squeeze(my_predicted_image)),].decode(\"utf-8\") +  \"\\\" picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What to remember from this assignment:**\n",
    "1. Preprocessing the dataset is important.\n",
    "2. You implemented each function separately: initialize(), propagate(), optimize(). Then you built a model().\n",
    "3. Tuning the learning rate (which is an example of a \"hyperparameter\") can make a big difference to the algorithm. You will see more examples of this later in this course!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you'd like, we invite you to try different things on this Notebook. Make sure you submit before trying anything. Once you submit, things you can play with include:\n",
    "    - Play with the learning rate and the number of iterations\n",
    "    - Try different initialization methods and compare the results\n",
    "    - Test other preprocessings (center the data, or divide each row by its standard deviation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bibliography:\n",
    "- http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/\n",
    "- https://stats.stackexchange.com/questions/211436/why-do-we-normalize-images-by-subtracting-the-datasets-image-mean-and-not-the-c"
   ]
  }
 ],
 "metadata": {
  "coursera": {
   "course_slug": "neural-networks-deep-learning",
   "graded_item_id": "XaIWT",
   "launcher_item_id": "zAgPl"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
